We show that a typical Besicovitch set \(B\) has intersections of measure zero with every line not contained in it. Moreover, every line in \(B\) intersects the union of all the other lines in \(B\) in a set of measure zero.
"The Intersection of Typical Besicovitch Sets with Lines." Real Anal. Exchange 45 (2) 453 - 464, 2020. https://doi.org/10.14321/realanalexch.45.2.0453